PaperlayerView exact revision on arXiv

Source-linked AI summary

Dual-Function MIMO Radar Communications System Design Via Sparse Array Optimization

Xiangrong Wang, Aboulnasr Hassanien, Moeness Amin

arXiv:1808.04940v1eess.SP

TL;DR

Spectrum congestion motivates dual-function radar–communications systems that share radar resources with communications. This paper embeds information through sparse-array configuration and waveform–antenna reordering, with a regularized selection scheme addressing implementation issues. The proposed techniques support megabits-per-second data rates with low symbol error rate and improved robustness to communication-angle estimation error.

  • Problem

    Spectrum congestion and competition for frequency bandwidth motivate sharing radar resources, spectrum, and platform hardware with communications.

  • Method

    The paper embeds communication symbols using sparse transmit-array antenna selection, hybrid antenna selection and waveform–antenna permutation, and regularized selection.

  • Results

    The hybrid strategy achieves a megabits-per-second data rate with low symbol error rate, while regularized selection provides strong robustness against communication receiver angle estimation error.

  • Takeaways & Limitations

    Sparse-array configurations and waveform diversity can support concurrent communication information embedding and MIMO radar operation.

Abstract

from arXiv · show

Spectrum congestion and competition over frequency bandwidth could be alleviated by deploying dual-function radar-communications systems, where the radar platform presents itself as a system of opportunity to secondary communication functions. In this paper, we propose a new technique for communication information embedding into the emission of multiple-input multiple-output (MIMO) radar using sparse antenna array configurations. The phases induced by antenna displacements in a sensor array are unique, which makes array configuration feasible for symbol embedding. We also exploit the fact that in a MIMO radar system, the association of independent waveforms with the transmit antennas can change over different pulse repetition periods without impacting the radar functionality. We show that by reconfiguring sparse transmit array through antenna selection and reordering waveform-antenna paring, a data rate of megabits per second can be achieved for a moderate number of transmit antennas. To counteract practical implementation issues, we propose a regularized antenna selection based signaling scheme. The possible data rate is analyzed and the symbol/bit error rates are derived. Simulation examples are provided for performance evaluations and to demonstrate the effectiveness of proposed DFRC techniques.

I. INTRODUCTION

The paper develops DFRC techniques that embed communication symbols through reconfigurable sparse transmit arrays while retaining MIMO radar operation. It combines antenna selection, waveform diversity, and waveform–antenna reordering to address spectrum sharing and practical implementation concerns.

  • Motivation: DFRC systems share radar resources, spectrum, bandwidth, and platform hardware with communication functions in congested RF environments.The radar platform can serve as a system of opportunity for secondary communications during radar operation.
  • Motivation: Fixed uniform arrays overlook spatial degrees of freedom that can help manage interference and support joint radar–communications operation.Sparse arrays are also presented as a way to reduce system complexity and cost while retaining array benefits.
  • Contributions: The paper proposes antenna selection and hybrid selection–permutation signaling to embed symbols in transmit-array configurations and waveform–antenna associations.The hybrid strategy is intended to achieve high data rate and reduce symbol error rate.
  • Practical considerations: Practical signaling must account for antenna-selection hardware constraints and communication-angle effects, including angular ambiguities and degraded performance at small receiver angles.The regularized scheme targets implementation issues and robustness against communication-angle estimation error.
  • System configuration: The joint platform uses M transmit antennas, K<M RF front-ends, selectable antennas, and K orthogonal waveforms transmitted through the selected antennas.The communication receiver is assumed to know the receiver direction, while radar processing uses matched filtering for individual waveforms.
  • Signal model: Sparse transmit-array configurations provide spatial degrees of freedom that can be combined with waveform design in the temporal domain for concurrent symbol embedding and MIMO radar functions.The sparse steering vector is determined by antenna positions and their induced phases.

III. ANTENNA SELECTION BASED SIGNALING STRATEGY FOR DFRC SYSTEMS

The antenna-selection signaling strategy uses selected sparse transmit-array steering vectors as communication symbols while transmitting orthogonal waveforms for MIMO radar.

  • Antenna selection based signaling: Antenna selection enables communication symbols to be embedded into the transmit array configuration.The selected antennas transmit independent orthogonal waveforms concurrently with radar operation.

A. Information Embedding Scheme

Each selectable K-antenna subset defines a distinct sparse-array steering vector and communication symbol. The receiver recovers the selected subset from matched-filtered waveform observations.

  • Array selection: The full transmit array has steering vector a(θ), and applying selection matrix P(τ) produces the steering vector of the selected subarray.P(τ) contains one active entry per row corresponding to a selected antenna.
  • Symbol construction: Selecting K antennas from M creates L = C(M,K) possible antenna subsets, with each subset corresponding to a unique selection matrix and sparse steering vector.Each subset can represent a communication symbol containing N_b bits.
  • Receiver processing: Matched filtering with the K orthogonal waveforms produces communication observations that are scaled and noisy selections of the full steering vector.The communication receiver uses these observations to recover the selected sparse array and decode its associated symbol.

B. Detection of communication Symbols

Communication symbols are embedded through selected sparse-array steering vectors and detected by nearest-dictionary matching. The symbol rate equals the radar pulse repetition frequency, while phase rotation mitigates angular ambiguities without disrupting radar operation.

  • Symbol dictionary: A dictionary of L symbols is formed from steering vectors of selected sparse arrays aimed at the communication receiver.The dictionary cardinality determines communication capacity, and using a subset of available symbols can improve noise immunity.
  • Symbol transmission: Each radar pulse maps Nb information bits to a decimal index, selects K antennas, and transmits the corresponding orthogonal waveforms.The scheme assumes accurate channel estimation, with periodic training sequences available for updating the estimate and phase synchronization.
  • Symbol detection: The receiver detects a symbol by selecting the dictionary entry with minimum Euclidean distance from the estimated steering vector.Detection requires LK complex multiplications, so computational complexity grows with the data rate.
  • Data rate: Nb × fPRF bit per second is the resulting data rate because one communication symbol is transmitted per radar pulse.The symbol rate is identical to the pulse repetition frequency.
  • Angular ambiguity: When the receiver angle exceeds the maximal spread angle, multiple antennas may share phase values modulo 2π, creating angular ambiguities.At broadside, all steering-vector entries are one, so antenna selection cannot embed information; small angles can also yield poor performance with the full bit count.
  • Ambiguity mitigation: Additional per-antenna phase rotations uniformly distribute phases around the unit circle at the receiver angle while preserving waveform orthogonality and normal radar operation.This phase rotation enables ambiguity mitigation and supports a suitable symbol dictionary for any receiver spatial angle.

D. Symbol Error Rate

The paper analyzes symbol detection as distance-based decoding among phase-rotated steering-vector codes. It derives correct-detection and symbol-error bounds using the geometry of M-ary PSK phase constellations while accounting for radar beampattern requirements.

  • Symbol representation: After phase rotation, each dictionary symbol contains K phases selected from M uniformly spaced values around the unit circle.The resulting symbol representation is independent of the receiver angle because the additional phase rotations remove that dependence.
  • Detection criterion: A received symbol is correctly detected when its distance to the transmitted code is smaller than its distance to every competing dictionary code.This criterion allows correct symbol detection even when noise moves an individual phase closer to another constellation point.
  • Error analysis: Each phase term follows an M-ray PSK geometry with angular separation γ = 2π/M, enabling phase-level error analysis using SNR ρ.The average M-ary PSK symbol-error expression is used to obtain a lower bound on vector detection probability.
  • Joint design: The symbol subset should jointly maximize communication-code distances and maintain a satisfactory radar transmit beampattern.The same K orthogonal waveforms are transmitted during each PRI, avoiding Doppler coherency degradation associated with the cited waveform-modulation scheme.

E. Selection of Constellation Symbols

Constellation design selects a subset of sparse-array symbols using communication separation and radar beampattern criteria. The resulting nonconvex selection problems are handled with sequential convex programming and sparse binary antenna variables.

  • Communication criterion: The communication criterion selects Lb = 2^Nb symbols from L candidates to maximize the minimum distance between dictionary symbols.For even M, the two farthest initial symbols are center-symmetric and have distance ∥ã1 − ã2∥2 = 4K.
  • Antenna selection: A binary selection vector z chooses exactly K antennas, with one denoting selection and zero denoting discard.The selected nonzero entries of diag(z)a form a symbol in the communication subset.
  • Regularized selection: The optimization trades symbol distance against the binary property of z through parameter µ, with µ = 1 assigning equal importance.The formulation combines distance-based constellation design with constraints enforcing antenna selection structure.
  • Radar criterion: Radar-oriented selection seeks sparse transmit configurations whose combined transmit-receive beampattern concentrates power within the desired angular sector Θ.The receive array is fixed, while the transmit configuration and beamforming weights determine the overall MIMO radar beampattern.
  • Beampattern constraints: Beampattern constraints specify mainlobe phase-profile fidelity, bounded ripple, sidelobe limits, and block-sparse weight structure.The matrices Jm extract antenna-associated weight blocks for enforcing selection-related constraints.
  • Optimization procedure: Sequential convex programming repeatedly linearizes the concave objective to produce convex subproblems for symbol selection.Because SCP is a local heuristic dependent on its initial point, multiple feasible initializations can be used to construct the dictionary.

IV. HYBRID SELECTION AND PERMUTATION BASED SIGNALING STRATEGY FOR DFRC SYSTEMS

The hybrid strategy embeds symbols through both sparse transmit-antenna selection and reordering of orthogonal waveform assignments. Its selected-permutation steering-vector codes form a large constellation while preserving the primary MIMO radar operation.

  • Hybrid signaling principle: The receiver need not pin each orthogonal waveform to a specific antenna, enabling waveform reassignment across selected transmit antennas between PRIs.The radar knows the waveform–antenna pairing, so reordering can restore the coherent MIMO radar data structure.
  • Performance and optimization: The hybrid scheme can achieve megabits-per-second data rates with a moderate number of transmit antennas by combining selection with waveform permutation.The number of transmitted message bits per pulse and the resulting data rate are determined from the combined dictionary.
  • Signal construction: The hybrid signal is represented by a K × M selection matrix P(τ) and a K × K permutation matrix Q(τ), with M(τ) = Q(τ)P(τ).The selected antennas transmit independent waveforms during each radar pulse.
  • Code dictionary: Selected-permutation steering vectors use the ordered phases induced by antenna positions as communication codes.The communication receiver recovers the selection and ordering from the matched-filter output by comparing the estimated vector with the code dictionary.
  • Code dictionary: The dictionary contains K! permutations for each selected sparse subarray, increasing the available symbol set beyond antenna selection alone.Phase rotations can also be applied to mitigate angular ambiguity and improve communication performance.
  • Performance and optimization: The hybrid scheme can significantly reduce symbol error rate relative to selection-only signaling by increasing distances between selected symbols.Joint dictionary design is difficult because selection and permutation constraints make the optimization highly non-convex, and exhaustive enumeration is prohibitively expensive.

V. REGULARIZED SELECTION BASED SIGNALING STRATEGY FOR DFRC SYSTEMS

The regularized strategy embeds one bit per antenna subgroup by selecting one of two adjacent antennas, while phase rotations support BPSK-like detection. This constrained design addresses hardware and radar-transparency issues associated with unrestricted selection.

  • Regularized selection: Regularized antenna selection restricts each subgroup to one selected antenna, avoiding arbitrary K-antenna subsets that can burden the antenna-selection hardware.The scheme uses M = 2K uniformly spaced antennas divided into K adjacent-antenna subgroups.
  • Regularized selection: Each adjacent-antenna subgroup represents one bit: selecting the first antenna encodes 0, while selecting the second encodes 1.The restriction guarantees a constant K selected transmit antennas.
  • Detection: Phase rotations are pre-multiplied with the orthogonal waveforms to decouple communication performance from the receiver arrival angle without disrupting radar operation.The rotated waveforms preserve orthogonality, and the receiver deciphers each bit from the received-signal phase after matched filtering.
  • Rate: The scheme embeds K bits during each radar pulse, so its data rate is determined by K and the pulse-repetition frequency.The paper expresses the rate in bits per second from the number of embedded bits per pulse.
  • Error performance: The regularized selection strategy has the same bit error rate as BPSK.Its symbol error rate is expressed in terms of the bit error rate because all K bits must be correctly detected for the K-bit symbol to be correct.
  • Symbol dictionary: The regularized scheme has 2^K symbols, requires no further symbol-subset selection, and keeps antenna–waveform associations fixed.Its minimum-distance symbol pairs differ by switching one antenna within one subgroup, while maximum-distance pairs switch antennas in all K subgroups.

VI. SIMULATIONS

Simulations use a 16-antenna transmit ULA and select 8 antennas per pulse to embed one communication symbol while continuing radar operation. Performance is evaluated primarily through symbol error rate versus SNR.

  • Simulation setup: The simulated radar has M = 16 transmit antennas in a ULA with 0.25-wavelength inter-element spacing.The receiver array is a 10-antenna ULA.
  • Simulation setup: K = 8 transmit antennas are selected during each PRI to embed one communication symbol while performing radar operation.Unless otherwise stated, performance is shown as symbol error rate as a function of SNR.

A. Example 1: Antenna Selection based signaling Scheme

Example 1 embeds symbols by selecting sparse transmit subarrays from dictionaries designed either to preserve radar beampatterns or maximize communication separation. The radar-favored dictionary yields expected SER behavior, while the communication-favored dictionary improves SER at the cost of greater beampattern variation.

  • Signaling configuration: 13 bits per symbol is the maximum from 12870 possible 8-antenna selections, while evaluated dictionaries support 1, 2, 4, or 8 bits per symbol.The dictionaries contain 2, 4, 16, or 256 subarrays, respectively.
  • Dictionary construction: 256 configurations are selected offline either for smallest radar-beam peak ripples in Dr or maximum inter-symbol Euclidean distance in Dc.Both scenarios require a peak sidelobe level of −20 dB.
  • Dictionary construction: Dr produces nearly identical sparse-array power patterns with small mainlobe ripple, whereas larger dictionaries can deviate from the nominal mainbeam.The radar-prioritized dictionary emphasizes beampattern consistency.
  • Communication performance: SER increases as SNR decreases for Dr, reaching approximately 0.5 at −20 dB for 1 bit per symbol.At low SNR, noise causes approximately equal probabilities of correct and erroneous symbol detection.
  • Communication performance: Dc provides better SER performance than Dr because its configurations are designed to enhance communication performance.This improvement accompanies larger differences between corresponding beampatterns and increased mainlobe ripple.

B. Example 2: Hybrid Selection and Permutation based signaling Scheme

Example 2 combines sparse-array selection with waveform-antenna permutation to enlarge symbol separation. Example 3 introduces regularized selection for practical implementation, trading some performance for improved robustness to communication-angle estimation error.

  • B. Example 2: Hybrid Selection and Permutation based signaling Scheme: Permuting Dc configurations produces Dp, whose minimum inter-symbol distance is much larger than those of Dr and Dc.The minimum distance directly determines communication accuracy in the cited comparison.
  • B. Example 2: Hybrid Selection and Permutation based signaling Scheme: The hybrid scheme significantly improves communication performance, especially at 8 bits per symbol.SER is evaluated using randomly generated symbols and one communication symbol per PRI.
  • B. Example 2: Hybrid Selection and Permutation based signaling Scheme: 28 bits per symbol are available from antenna selection combined with all waveform-antenna permutations.The evaluation considers 1, 2, 4, and 8 bits per symbol.
  • C. Example 3: Regularized Selection based signaling Scheme: Regularized selection divides a 16-antenna ULA into eight two-antenna subgroups and selects one antenna per subgroup each radar pulse.The scheme creates 2^8 = 256 symbols without symbol-subset selection.
  • C. Example 3: Regularized Selection based signaling Scheme: Regularized selection has inferior communication performance to the hybrid strategy but outperforms antenna selection using Dr and Dc.Its sparse-array power patterns are worse than Dr's but better than those of the compared communication-oriented dictionary.
  • C. Example 3: Regularized Selection based signaling Scheme: Regularized selection is more robust than the hybrid scheme to communication-receiver angle estimation error.The comparison varies the standard deviation of normally distributed receiver-angle error across 1, 2, 4, and 8 bits per symbol.

VII. CONCLUSIONS

The paper develops sparse-array signaling schemes for dual-function MIMO radar communications. It reports high data rate with low symbol error rate for hybrid selection and permutation, and strongest angle-error robustness for regularized selection.

  • VII. CONCLUSIONS: Three schemes embed communication information through antenna selection, hybrid selection and permutation, and regularized selection alongside waveform diversity.The schemes use transmit-array configurations for symbol embedding in dual-function MIMO radar communications.
  • VII. CONCLUSIONS: Hybrid selection and permutation achieves a megabits-high data rate with low symbol error rate.This is the paper's stated headline communication result.
  • VII. CONCLUSIONS: Regularized selection provides the best robustness against communication-receiver angle estimation error.The scheme was proposed from the viewpoint of practical implementation.
  • VII. CONCLUSIONS: Simulation results validate sparse-array deployment for communication-performance enhancement without impacting primary radar functions.The conclusion frames this as successful deployment in dual-function MIMO radar communications systems.
Loading 1808.04940v1…